By HaRav Shimon Anshin shlit”a
1] The Schach of the Sukkah as well as the Lulav should not be treated in a disrespectful manner after the time of their Mitzvah has passed, and they should not be disposed of into a disgraceful place. Still, they do not require genizah, to be specially set away as seforim do. They should not be thrown directly into the garbage, but if they happen to get thrown out as a result of lack of genizah, there is nothing to worry about.
It is wrong for people to leave their schach after Sukkos outside, in places where people step all over them, even though they are not in the trash. One should not even use the walls of the Sukkah for inappropriate use after Sukkos. (summary of Rem”a and Mishna Berura 21:1, ibid: 6-7, and Mishna Berura 678:24)
2] We learn the following Halachos from the above:
A] It is forbidden to dispose of schach into the trash can. Even though this halachah is clearly stated, still, many people don’t realize this and throw out their schach into the garbage, without knowing that it is absolutely forbidden!
B] Similarly, it’s prohibited to place them around the area of trash cans. There are people who are careful not to put the schach directly into the garbage cans yet they place them around the cans. Seemingly they should be able to rely on the Mishna Berura which says, “If as a result of not putting them specially away they get thrown out, there is nothing to worry about.” Nevertheless, I feel that they really don’t have what to rely on, because that’s only referring to schach getting thrown out because of their not being placed into genizah, not putting them around the garbage where they will certainly be taken afterwards into the trash. Sometimes they end up sitting there for a couple of days, and end up being totally neglected.
C] One is not allowed to place the schach where people will step on them. Besides causing others who don’t know better to mistreat the schach, it is also bothering those people who know to be careful in that they have to now go around it.
D] It is forbidden to step on schach, even if the owner already transgressed the above and put them in a place where people walk.
E] As for Sukkah decorations, there are those who say that it’s fitting that they not be thrown into the garbage; nevertheless, if they are well wrapped in a bag, they can then be put into the garbage.
3] The Shulchan Aruch writes in 664:8, “There are those who say that the Hoshana (Arava) in the Lulav as well as the Arava of Hoshana, even though they have been disposed of, they should not be stepped upon. It’s Halachos are as explained above 21:1.”
The Halachos which arise from the Shulchan Aruch as well as Mishna Berurah ibid: 28-29 are as follows:
A] The Four Minim – it’s forbidden to mishandle them, and they therefore should not be placed in the garbage or stepped upon, as we explained above.
B] Hoshanos – have the same rules as the Four Minim. Therefore, it’s befitting to sweep up the floor of the shul from the Hoshana leaves immediately after their use, in order that no one comes to step on them.
The custom to throw them on top of the ‘Aron Kodesh’ has no source in the ancient works. There are those who have questioned it because of the prohibition to make use of an Aron Kodesh, of which the rules of properly respect of its sanctity are very strict. The responsibility falls on the gabbaim that care should at least be taken that they do not afterwards end up thrown in the garbage.
People cannot be expected to act otherwise, since they have already become accustomed to this.
C] The Rings and Holders- should not be treated in an inappropriate way, since they are easily recognized to have been used for a Mitzvah.
D] The Esrog box and Lulav holder – it is better not mishandle them, especially if pesukim or parts of pesukim are written on them, which would require genizah. (The words pri eitz hadar do not require genizah)
E] Keeping the Four Minim in the house – It is brought in seforim that keeping the Four Minim in a home serves as a protection for it. It is also well known that the Rebbe says that Hoshanas are a protection while travelling.
Therefore, it’s better not to dispose of them in any way, on the contrary, to keep them in the house.
Why even burn them with the chametz and lose their protection? However, in order to keep this custom, it is possible to burn the Four Minim from
last year and to keep the ones from this year.
As this is a translation of the original Hebrew, if you unclear on any of the Laws outlined herein
in any way whatsoever, please consult with a Posek (Halachic Authority).